Using Automatic Vectorization

Vectorization Speed-up

Where does the vectorization speedup come from? Consider the following sample code fragment, where a, b and c are integer arrays:

do I=1,MAX
    C(I)=A(I)+B(I)
    end do

If vectorization is not enabled (that is, you compile using O1 or [Q]vec- options), for each iteration, the compiler processes the code such that there is a lot of unused space in the SIMD registers, even though each of the registers could hold three additional integers. If vectorization is enabled (compiled using O2 or higher options), the compiler may use the additional registers to perform four additions in a single instruction. The compiler looks for vectorization opportunities whenever you compile at default optimization (O2) or higher.

To get information on whether a loop was vectorized or not, enable generation of the optimization report using the options Qopt-report:1 Qopt-report-phase:vec (Windows) or qopt-report=1 qopt-report-phase=vec (Linux and OS X) options. These options generate a separate report in an *.optrpt file that includes optimization messages. In Visual Studio, the program source is annotated with the report's messages, or you can read the resulting .optrpt file using a text editor. A message appears for every loop that is vectorized, such as:

> ifort /Qopt-report1 matvec.f90
> type matvec.optrpt
…
   LOOP BEGIN at C:\Projects\vec_samples\matvec.f90(38,6)
      remark #15300: LOOP WAS VECTORIZED
   LOOP END

The source line number (38 in the above example) refers to either the beginning or the end of the loop.

To get details about the type of loop transformations and optimizations that took place, use the [Q]opt-report-phase option by itself or along with the [Q]opt-report option.

How significant is the performance enhancement? To evaluate performance enhancement yourself, run vec_samples:

1. Open an Intel® Compiler command line window.

   • On Windows*: Under the Start menu item for your Intel product, select an icon under Compiler and Performance Libraries > Command Prompt with Intel Compiler

   • On Linux* and OS X*: Source an environment script such as compilervars.sh or the compilervars.csh in the <installdir>/bin directory and use the attribute appropriate for the architecture.

2. Navigate to the <install-dir>\Samples\<locale>\Fortran\ directory. On Windows, unzip the sample project vec_samples.zip to a writable directory. This small application multiplies a vector by a matrix using the following loop:

   Example: Vector Matrix Multiplication
   do i=1,size1 c(i) = c(i) + a(i,j) * b(j) end do

3. Build and run the application, first without enabling auto-vectorization. The default O2 optimization enables vectorization, so you need to disable it with a separate option. Note the time taken for the application to run.

   Example: Building and Running an Application without Auto-vectorization
   // (Linux* and OS X* with EDG compiler) ifort -no-vec driver.f90 matvec.f90 -o NoVectMult ./NoVectMult
   // (Windows*) ifort /Qvec- driver.f90 matvec.f90 /exe:NoVectMult NoVectMult

4. Now build and run the application, this time with auto-vectorization. Note the time taken for the application to run.

   Example: Building and Running an Application with Auto-vectorization
   // (Linux* and OS X* with EDG compiler) ifort driver.f90 matvec.f90 -o VectMult ./VectMult
   // (Windows*) ifort driver.f90 matvec.f90 /exe:VectMult VectMult

When you compare the timing of the two runs, you may see that the vectorized version runs faster. The time for the non-vectorized version is only slightly faster than would be obtained by compiling with the O1 option.

Obstacles to Vectorization

The following do not always prevent vectorization, but frequently either prevent it or cause the compiler to decide that vectorization would not be worthwhile.

• Non-contiguous memory access: Four consecutive integers or floating-point values, or two consecutive doubles, may be loaded directly from memory in a single SSE instruction. But if the four integers are not adjacent, they must be loaded separately using multiple instructions, which is considerably less efficient. The most common examples of non-contiguous memory access are loops with non-unit stride or with indirect addressing, as in the examples below. The compiler rarely vectorizes such loops, unless the amount of computational work is large compared to the overhead from non-contiguous memory access.

  Example: Non-contiguous Memory Access
  ! arrays accessed with stride 2 do I=1,SIZE,2; B(I)=B(I)+(A(I)*X(I)); end do ! inner loop accesses a A with stride SIZE do J=1,SIZE do I=1,SIZE B(I)=B(I)+(A(J,I)*X(J)) end do end do ! indirect addressing of x X using index array INDX do I=1,SIZE,2; B(I)=B(I)+(A(I)*X(INDX(I))); end do

  The typical message from the vectorization report is: vectorization possible but seems inefficient, although indirect addressing may also result in the following report: Existence of vector dependence.

• Data dependencies: Vectorization entails changes in the order of operations within a loop, since each SIMD instruction operates on several data elements at once. Vectorization is only possible if this change of order does not change the results of the calculation.

  • The simplest case is when data elements that are written (stored to) do not appear in any other iteration of the individual loop. In this case, all the iterations of the original loop are independent of each other, and can be executed in any order, without changing the result. The loop may be safely executed using any parallel method, including vectorization. All the examples considered so far fall into this category.

  • When a variable is written in one iteration and read in a subsequent iteration, there is a “read-after-write” dependency, also known as a flow dependency, as in this example:

    Example: Flow Dependency
    A(2)=A(1)+1 A(3)=A(2)+1 A(4)=A(3)+1 A(5)=A(4)+1

    So the value of j gets propagated to all A(J). This cannot safely be vectorized: if the first two iterations are executed simultaneously by a SIMD instruction, the value of A(2) is used by the second iteration before it has been calculated by the first iteration.

  • When a variable is read in one iteration and written in a subsequent iteration, this is a write-after-read dependency, also known as an anti-dependency, as in the following example:

    Example: Write-after-read Dependency
    do J=2,MAX; A(J-1)=A(J)+1; end do ! this is equivalent to: A(1)=A(2)+1 A(2)=A(3)+1 A(3)=A(4)+1 A(4)=A(5)+1

    This write-after-read dependency is not safe for general parallel execution, since the iteration with the write may execute before the iteration with the read. However, for vectorization, no iteration with a higher value of j can complete before an iteration with a lower value of j, and so vectorization is safe (that is, it gives the same result as non-vectorized code) in this case. The following example, however, may not be safe, since vectorization might cause some elements of A to be overwritten by the first SIMD instruction before being used for the second SIMD instruction.

    Example: Unsafe Vectorization
    do J=1,MAX A(J-1)=A(J)+1 B(J)=A(J)*2 end do ! this is equivalent to: A(1)=A(2)+1 A(2)=A(3)+1 A(3)=A(4)+1 A(4)=A(5)+1

  • Read-after-read situations are not really dependencies, and do not prevent vectorization or parallel execution. If a variable is unwritten, it does not matter how often it is read.

  • Write-after-write, or ‘output’, dependencies, where the same variable is written to in more than one iteration, are in general unsafe for parallel execution, including vectorization.

  • One important exception, that apparently contains all of the above types of dependency:

    Example: Dependency Exception
    MYSUM=0 do J=1,MAX; MYSUM = MYSUM + A(J)*B(J); end do

    Although MYSUM is both read and written in every iteration, the compiler recognizes such reduction idioms, and is able to vectorize them safely. The loop in the first example was another example of a reduction, with a loop-invariant array element in place of a scalar.

    These types of dependencies between loop iterations are sometimes known as loop-carried dependencies.

    The above examples are of proven dependencies. The compiler cannot safely vectorize a loop if there is even a potential dependency. Consider the following example:

    Example: Potential Dependency
    real, pointer :: A(:),B(:),C(:) … do I=1,SIZE; C(I)=A(I)*B(I); end do

    In the above example, the compiler needs to determine whether, for some iteration I, C(I) might refer to the same memory location as A(I) orB(I) for a different iteration. Such memory locations are sometimes said to be aliased. For example, if A(I) pointed to the same memory location as C(I-1), there would be a read-after-write dependency as in the earlier example. If the compiler cannot exclude this possibility, it will not vectorize the loop unless you provide the compiler with hints. You can also avoid this problem by making the arrays ALLOCATABLE instead of POINTER, as the compiler knows these cannot be aliased.